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Concept Detail
Maths / Lines and Angles / Linear Pair
(A Brief Glimpse of ABHYAS Content - Have aLook !!!!)

LINEAR PAIR

It is a pair of adjacent angles in which the non common arms form a Straight Lines.

 A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
 Illustration:  Find the values of the angles x, y and z in each of the following: Solution:  $\large 80^{\circ}+x+30^{\circ}=180^{\circ}$    [Angles on a straight line] 110 + x = 180 :   x = 180 - 110 = 70  $\large 80^{\circ}+y=180^{\circ}$     [Linear pair] y = 180 - 80 = 100      (i) Also  Y + Z = 180    [Linear pair] 100 + Z = 180 : Z = 180 - 100 = 80

Illustration: Find the value of x if it forms a linear pair with angle whose measure is 118 degrees.

Solution: As x and angle 118 degrees forms a pair of linear angle. Hence we must have

$\dpi{80} \large x^{0}+118^{0}=180^{0}$

$\dpi{80} \large \therefore x^{0}=180^{0}-118^{0}$

$\dpi{80} \large \therefore x=62^{0}$

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